There have been a few posts on jobs in Palestine, but the Israelis make it nearly impossible to work there by not allowing visas. If you can deal with the hassles, you might try applying directly to them.

I knew a guy who taught in the West Bank on a volunteer program (though he did get a stipend).
Mind you, seeing how things were run there by the local authorities, turned him into one of the most pro-Israel people I've met in Turkey.

My point was that bringing the economic opportunities of English to the suffering people of the Holy Land may not be as glorious as one might expect. Doesn't really matter to what degree you blame the Israelis, Palestinians, or both; it seems like a pretty depressing situation.

That said, there are certainly volunteer opportunities, though I don't know what organization the guy I knew worked for (I'm not in contact with him anymore but I do know he was practicing but non-evangelical Christian, so it's probably neither one of those Israeli peace-through-understanding groups, nor a missionary organization). I keep seeing ads for "Teach for Palestine," which I won't link, since it seems to get bad reviews. Googling I also found some other interesting stuff, like Project Hope, which I only found one review for, but it's a positive one.

I doubt that there are many well-paid opportunities in the West Bank, for the same reason there aren't many well-paid opportunities in Lebanon. It's rebuilding from a war, and unlike Iraq and Libya, it has no oil. You can certainly forget about Gaza, since it's under sanctions.